Reddit reviews Methods of Logic

I don't know what others would recommend, but Quine's intro to logic is a classic text.

Quine's Methods of Logic and Mathematical Logic (in that order) have been my favorites, and I've heard good things about Tarski's Introducion to Logic: and the the Methodology of Deductive Sciences but have yet to get around to it.

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Really? Nolt's Logics? Besides the numerous errors, it's telling that the book has not come out in a second edition.

I think Quine's Methods of Logic remains a fantastic text, if it is a bit dated and filled with Quinean quirks. A more recent text, Ted Siders' Logic for Philosophy is also very good, although the exercises are sometimes quite difficult. I would combine Sider's text with a book on metalogic, since he skips over some of that. Kleene's Mathematical Logic is a classic text by a real giant in the history of 20th century logic. Those should keep someone busy for a good year of study. If you want to branch out, Graham Priest's Introduction to Non-classical Logics will get you started in modal, tense, epistemic, paraconsistent and dialethic logics, also by a contemporary giant in the field.

After that, I would go on to set theory, and stop when I had a grasp of forcing.

This is a classic logic text I used as an undergrad:

https://www.amazon.com/Methods-Logic-Willard-Orman-Quine/dp/0674571762/ref=pd_bxgy_14_img_2/144-3692070-4202828?_encoding=UTF8&pd_rd_i=0674571762&pd_rd_r=d2bce5e1-7920-11e9-bee9-f381f43bc426&pd_rd_w=wECMX&pd_rd_wg=tpHvf&pf_rd_p=a2006322-0bc0-4db9-a08e-d168c18ce6f0&pf_rd_r=MAZ7WGR0JV0HZMV097EC&psc=1&refRID=MAZ7WGR0JV0HZMV097EC

There's plenty of good resources online to do this, but I wanted to suggest to you the textbooks from which I taught myself Calculus in high school, and it's this series: http://www.amazon.com/s?ie=UTF8&keywords=Calculus&rh=n%3A283155%2Ck%3ACalculus%2Cp_lbr_one_browse-bin%3ARobert%20Blitzer&page=1

You probably aren't going to want to go out and spend a ton of money on these books, but if you can find old editions for cheap, I'd say it's worth your money. :)

Good luck with the math! Also, if you want to really start going proper math, another great book is: http://www.google.com/products/catalog?hl=en&q=foundations+of+math&gs_upl=165l1646l0l1837l19l11l0l1l1l1l265l2237l0.5.6l11l0&bav=on.2,or.r_gc.r_pw.r_cp.,cf.osb&biw=1032&bih=614&um=1&ie=UTF-8&tbm=shop&cid=6951129580330045396&sa=X&ei=ntjhTqyvDo7FswaP7aGgBA&ved=0CHoQ8wIwCg#ps-sellers

And if you're interested in the logical underpinnings of the really fun mathematics, another great place to look is: http://www.amazon.com/Methods-Logic-W-V-Quine/dp/0674571762

Sorry that these are all big expensive textbooks, but I wanted to share with you some of my favorite books. :)

Well I learned from these (undergraduate level):

The Power of Logic by Howard-Snyder, Howard-Snyder and Wasserman

and

Methods of Logic by Willard Van Orman Quine

I highly recommend both but Methods is not a good place to start. Excellent once you can handle yourself though. Unfortunately The Power of Logic is somewhat expensive.

By the way, here's an excellent online resource that you may find helpful.